Connection techniques have already been suggested to connect a tool spiral, for example consisting of hard metal, with as little expense as possible to a clamping cylinder so that an uninterrupted coolant supply is made possible to the inner coolant channels without stressing the connecting surfaces excessively. However, the previous solution suggestions had the drawback that, through them, an undetachable connection between the hard metal spiral and the clamping cylinder had to be made. Because of this, application possibilities of the tool were limited with increasing duration of use--i.e., after multiple grindings.